wages, runcationt and non-random sample selectionempirical implications of the theory the estimation...

IntroductionThe Human Capital Theory

Empirical Implications of the TheoryThe Estimation of the Returns to Education

Truncation & SelectionSummary

Wages, Truncation and Non-random Sample

Selection

Quantitative Microeconomics

R. Mora

Department of Economics

Universidad Carlos III de Madrid

R. Mora Nonrandom sample selection




Outline

1 Introduction

2 The Human Capital Theory

3 Empirical Implications of the Theory

4 The Estimation of the Returns to Education

5 Truncation & Selection





Motivation

One argument of why women partly specialize in domesticproduction is because their market wages are lower than thoseof their husbands

Beyond assuming they have di�erent productivities, there aremany alternative theories

Discrimination: employers and workers in mostly maleprofessions dislike working with women, so they are only willingto do it with some compensationWomen are less competitive than menThe most productive workers (also the worst) are malesWomen preferences and social roles drive them to work in asmall number of occupations, driving their wages down





The Human Capital Gender Gap Explanation

Another possible answer is provided by the human capital theory

Two stylized facts:

Women acquire less human capital than men (although thegap is fast decreasing)

Women's human capital has less market value

The human capital theory explains these two facts witheconomic incentives





What is Human Capital?

Skills which have market value and are obtained in a costly process

There are several ways to obtain human capital: education, lifeexperience, on-the-job training...

There are general skills (adequate for many jobs) andjob-speci�c skills

As with physical capital, human capital depreciates and can berented

In contrast to physical capital, human capital is person-speci�cso that it cannot be sold and it is zero at beginning of life





The Human Capital Theory in a Sentence

Individuals take Human Capital accumulation as an InvestmentDecision which a�ects their future wages





Experience increases income with age

Age

Income

w = β0+β1age+β2age2+ω





Education increases income given age

Age

Income

Low education

High education

w = β0+β1age+β2age2+β3educ+ ε





The Human Capital Investment Decision

Costs (fees, books, training wages) are incurred at thebeginning: C t0

Bene�ts (higher income & utility) are concentrated in thefuture: Bt0+s , s = 0,1,2, ...,T − t0

If total discounted future bene�ts ≥ current costs ⇒ Invest

T−t0∑s=0

Bt0+s

(1+rm)s≥ Ct0 ⇒Invest





The Internal Rate of Return

Internal Rate of Return

The interest rate r∗ such that the present value of the stream offuture bene�ts equals costs

T−t0∑s=0

Bt0+s

(1+r∗)s= Ct0

If r∗ ≥ rm⇒Invest





Si r∗ ≥ rm⇒ Invest

Years of Education

r *

rm

Optimal Yearsof Education

At equilibrium, r∗ = rm





Expected Labor Supply in the Life Cycle

Investments are more likely pro�table the larger the expectedworking life (more years to collect incomes)

women will invest less in education if they expect to work less

household-related duties: taking care of children and theelderly





Training in the Firm

General Human Capital (apprenticeship)

Workers may accept a low/no wage today if training leads tohigher wages in the future

Are women less likely to accept apprenticeships?

Speci�c Human Capital

Firms more likely to accept incurring the costs if worker islikely to stay in the �rm

Are women less likely to stay in the �rm?

If women are (perceived) to interrupt/slow down their careers more,then they will receive less training in the �rm





Di�erences in Education

Years of education are similar across gender

Fields of study are di�erent: human capital for women withhigh wR

do not depreciate fast with interruptionsis complementary to household productionincreases the husband's productivity





Mincer Equations

w = β0+β1exp+β2exp2+β3educ+ ε

Are returns to years of education equal for men and forwomen?

for the same type of education, they should

Are returns to years of working experience similar between menand women?

for the same type of experience, they should





Problems for Mincer Equations

Education and experience are chosen by each individual (theyare potentially endogenous)

Wages are only observable for those who choose to work(there is potential sample selection bias)

Wage data usually comes from �rms. In those cases, there isno information of those who choose not to work (truncation)

Here, we are going to

1 explain endogeneity for education2 present the truncation model3 present the selection model when the selection mechanism is

not driven by the dependent variable





Decision to Enter College

Elements for the decision to enter college

present net value of High School: E [vHS ]present net value of College: E [vCOL]

Person goes to college if E [vHS ]< E [vCOL]





Self-Selection into Education Bias

With observational data, individuals self-select into essentiallydi�erent groups:

For those who go to college: E [vHS |col ]≤ E [vCOL|col ]For those who do not go to college: E [vHS |hs]> E [vCOL|hs]

But

E [vcol |col ]−E [vhs |hs] = {E [vcol ]−E [vhs ]}+{E [vcol |col ]−E [vcol ]}+{E [vhs ]−E [vhs |hs]}





A Numerical Example with Two Periods

wageHS wageCOL

Bill 20,000¿ 40,000¿

Wendy 15,000¿ 41,000¿

PVHS(Bill) = 20+20/1.1= 38.1> 36.7= 0+40/1.1= PVCOL(Bill)

PVHS(Wendi) = 15+15/1.1= 28.6> 37.3= 0+41/1.1=PVCOL(Wendy)

returns to college 6= 37.3−38.1< 0





Mincer Equations and The Returns to Education

w = β0+β1exp+β2exp2+β3educ+ ε

ε includes unobservable wage e�ects from personalcharacteristics, such as innate ability

educ is chosen so that r∗ = rm, that is, educ re�ects to someextent wage factors known by the worker but unknown to theeconometrician, such as innate ability

OLS will be inconsistent, IV provides a possible solution





The Truncated Normal Regression Model

When wage data comes from �rms, there is no information of thosewho choose not to work

w = β0+β1exp+β2exp2+β3educ+ ε, ε|x ∼ N(0,σ2)

we only observe (wi ,expi ,educi ) if wi > wRi

(sample is not iid)

In the Tobit model, we have observations of everyone (thosewho work and those who do not work)

In the Truncated model, we only have observations of aselected sample (those who work)





Heckman's Selection Model

Wages are only observable for those who choose to work

we observe (wi ,expi ,educ i ) if si = 1, otherwise we observe zi

output equation: w = β0+β1exp+β2exp2+β3educ+ ε,

ε|x ∼ N(0,σ2)

participation equation: s = 1(γ ′z+ v)[ε

v

]∼ N

([00

],

[σ2u ρ

ρ σv²

])In Heckman's model, the participation equation is a di�erentprocess

Selection bias is a problem only if ρ 6= 0





Summary

the human capital theory views education and experience asinvestment decisions

the theory provides some testable mechanisms which mayexplain gender di�erences in human capital

however, the key test cannot be directly tested using standardols techniques because of endogeneity, sample selection, andsometimes, truncation

there are several ways to control for truncation or nonrandomsample selection


wages, runcationt and non-random sample selectionempirical implications of the theory the estimation...

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